A novel non-parametric statistical method in reliability theory: Mathematical characterization and analysis of asymmetric data in the fields of biological sciences and engineering

In recent decades, strategies devised to address challenges in life testing have noticeably veered away from those designed for related yet more intricate issues. The increasing complexity of data generated daily across practical fields has given rise to a novel realm in reliability that includes life classes and specific probability distributions. This study serves as an illustration of the effectiveness of integrating the goodness-of-fit technique into life testing quandaries, resulting in more efficient processes comparable to or surpassing traditional methods. Furthermore, these techniques exhibit potential for enhanced performance, particularly when dealing with smaller sample sizes. The comparison between the Exponential Better than Used in Increasing Convex in Laplace Transform Order (EBUCL) test statistic and a distinct goodness-of-fit test statistic upholds an approach leaning towards normalcy. Analysis encompassing powers, Pitman asymptotic effectiveness, and critical points, as well as the exploration of methodologies for handling suppressed data, has been undertaken. Additionally, a simulation study has been conducted to examine the study's motivations across various sample sizes. The results derived from our experiments hold practical implications for both bioscience and engineering sustainability data analyses.